Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D5×#15692425 |
| unambiguous semidirect product | C5⋊(C2×#15692425) |
| Fitting, derived, Hall | C5×C361 ⋊ C2×C9 |
| Hall | C5×#15692425 ⋊ C2 |
| Hall | D5×C361 ⋊ C9 |
| Sylow | C361 ⋊ C9×D5 |
| Sylow | C5 ⋊ C2×#15692425 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C361 | C2×C9 |
| Frattini | C19 | D5×#4296 |
| socle | C5×C19 | C2×#4296 |
| prime radical | D5×C361⋊C3 | C3 |
| cosocle | C5×C361⋊C3 | C2×C3 |
| LCS | G ▷ C5×C361 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1805 |
196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 15);